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Think about chess players: 95% of the time Magnus Carlsen immediately spots the right move to play (by his own numbers). The work is then backing it up by analysis or search.

If we didn't have a "hunch" in mathematics guiding us towards proofs or interesting results, we would be doing a completely random walk, or be brute forcing the search space, which would never lead anywhere interesting.

Sure, this hunch may be stronger with some people than others, but it mostly just comes from experience.




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